Chance and probability

Probability means the likelihood of something happening. For example, what is the probability that:

• There will be warm weather tomorrow?
• My parents will be upset when they see my school report?
• I will pass this test?
• Someone will make an insurance claim?

Probability or the chance that something will happen can be expressed in a number between 0 (that which is impossible i.e. no chance of happening) to 1 (that which is certain).

The calculation of probability is:

• Number of ways it can happen divided by the total number of outcomes.

Let's look at a die numbered 1 to 6, rolling once for a 6.

There is 1 way in which that can happen (rolling a 6) and there are 6 outcomes (1, 2, 3, 4, 5, 6). Therefore, the chance that you will roll a 6 in one roll of a die is one-sixth (1/6).

Let's also look at 2 dice rolling where both roll numbers that total to 4.

• How many ways in which that can happen? 3 ways. Here are possible ways (2,2) (1,3) (3,1).
• How many outcomes when you roll 2 dice = 36. There are 6 possibilities when rolling die 1 and for each outcome (1 to 6) there are also 6 possibilities that die 2 will roll. Therefore 6 x 6 = 36.
• Probability is 3 / 36 = 8.33%

Example Question/s

Watch video for explanation of the following question/s:

What is the probability of getting 2 heads when tossing 2 coins (assuming a coin has two faces, one heads and one tails)?

A three-quarters B a half C a quarter D five sixths E None of these

A game show contestant must jump blindfolded into a pool filled with a thousand balloons that are coloured red, green or white. The contestant must select a white balloon to win. The ratio of red to green to white balloons is 3:7:10. What is the chance that the game show contestant will select a white balloon?

A 10 B 1 C a half D one-tenth E None of these

Key Rules to remember

• 0 means no chance and 1 means certainty
• Probability is calculated as possible number of ways divided by total outcomes.

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let's get started on your practice questions.